By using a so-called extended double (ED)-complex method, the previously found doubleness symmetry of the dimensionally reduced Einstein–Kalb–Ramond (EKR) theory is further exploited. A 2d × 2d matrix double-complex H-potential is constructed and the field equations are written in a double-complex formulation. A pair of ED-complex Hauser–Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new double hidden symmetry transformations for the EKR theory are given. These symmetry transformations are verified to constitute double infinite-dimensional Lie algebras, each of which is a semidirect product of the Kac–Moody [Formula: see text] and Virasoro algebras (without center charges). These results demonstrate that the EKR theory under consideration possesses richer symmetry structures than previously expected, and the ED-complex method is necessary and more effective.